Ponencias (Ecuaciones Diferenciales y Análisis Numérico)
URI permanente para esta colecciónhttps://hdl.handle.net/11441/10836
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Ponencia Numerical solution of a Laplace equation with data in L1(Seminario matemático García de Galdeano, 2023-09-15) Casado Díaz, Juan; Chacón Rebollo, Tomás; Gómez Mármol, María Macarena; Girault, Vivette; Murat, François; Ecuaciones Diferenciales y Análisis Numérico; Palacios Latasa, Manuel Pedro; Trujillo, David; Torrens Iñigo, Juan José; Madaune-Tort, Monique; López de Silanes Busto, María Cruz; Sanz Sáiz, GerardoIn this work, we address the numerical solution of the Laplace equation with data in L1 by IP1 finite element schemes. Even if this is a simple problem, its analysis is difficult and requires new tools because finite element schemes are based on variational formulations which do not lend themselves to estimates in the L1 norm. The approach for analyzing this problem consists in applying some of the techniques that are used by Murat (cf. [5]) and Boccardo & Gallouet (cf. [2]) in constructing the renormalized solution of the problem. The key ingredient is the assumption that all the angles of the grid are acute; then the matrix of the system is an M matrix. Interestingly, with this sole assumption, we prove that uh tends to u in mesure in O.Ponencia Reduced order modelling for the optimization of CSP tower receivers and their cavities for high temperatura applications(The Open Publishing, 2023-12-19) Valverde, Juan; Galán Vioque, Jorge Francisco; Herruzo, Juan Carlos; Rubino, Samuele; Chacón Rebollo, Tomás; Núñez Fernández, Carlos; Ecuaciones Diferenciales y Análisis NuméricoWe present a Reduced Order Method approach to the heat exchange and loses in a simulated 3D cavity of CSP tower receivers. We validate the method in a 2D Boussinesq model problem for natural convection monitoring temperature, pressure and velocity for different values of the Rayleigh number. For the 3D problem of heat loses estimation we compute the snapshots with Ansys Fluent in a realistic model of a cavity with wind velocity and wall temperatures as varying parameters. The reduction in computational time can be up to four orders of magnitude with relative errors of 10^-5.Ponencia Residual Data-Driven Variational Multiscale Reduced Order Models for Convection-Dominated Problems(MATHMOD, 2025) Koc, Birgul; Rubino, Samuele; Chacón Rebollo, Tomás; Iliescu, Traian; Ecuaciones Diferenciales y Análisis NuméricoPonencia Two results on the control of fluids(Universidad de Oviedo, 2024-06-24) Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; Gallego Amez, Rafael; Mateos Alberdi, Mariano José; FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo SoftwareThis talk is devoted to recall and comment two results recently obtained concerning the control of viscous fluids. In general terms, we fix an initial state and we try to find internal or boundary data such that an associated solution vanishes at a prescribed time. Among others, we will consider fluids modeled by coupled systems of the Boussinesq kind. It will be seen that, under some circumstances, the systems are controllable or “quasi-controllable” in an appropriate sense. We will also take a look at some minimal time control problems and will present several theoeretical and numerical results. Also, several open problems will be mentioned.Ponencia Sharp estimates of the one-dimensional boundary control cost for parabolic systems(American Mathematical Society, 2020) González Burgos, Manuel; Ouaili, Lydia; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo SoftwarePonencia Random dynamical systems to analyze different ways of modeling stochastic chemostats(2017) López de la Cruz, Javier; Caraballo Garrido, Tomás; Garrido Atienza, María José; Rapaport, Alain; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis estocástico de sistemas diferencialesIn this talk, some different ways of modeling stochastic chemostats will be presented in order to obtain much more realistic mathematical models which reflect a better approximation to the real ones. To this end, the main interests of biologists will be taken into account and some well-known stochastic processes will be used. After that, these stochastic chemostat models will be analyzed by using the modern techniques concerning the theory of random dynamical systems (RDSs): interesting results related to existence and uniqueness of global solution just like that existence of absorbing sets and existence and uniqueness of random pullback attractor will be stated and several numerical simulations that support this work will be also shown.Ponencia Pullback attractors to analyze the effect of random and stochastic disturbances in the chemostat model(2018) López de la Cruz, Javier; Caraballo Garrido, Tomás; Garrido Atienza, María José; Rapaport, Alain; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis estocástico de sistemas diferencialesIn this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern techniques concerning the theory of random dynamical systems. Particularly, the existence and uniqueness of global solution will be stated and the existence and uniqueness of pullback random attractor will be also proved. Thanks to a deeper analysis involving the internal structure of the pullback random attractor, we will be able to provide conditions to ensure the persistence of the microbial biomass, which is also the main goal pursued by biologists. Finally, several simulations will be shown to support the results proved throughout the talk and help us to decide which kind of noise is more appropriated to model the real chemostats.Ponencia Studying the long time dynamics of fermentation models: production of dry and sweet wine(2020) López de la Cruz, Javier; Colucci, Renato; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis estocástico de sistemas diferencialesIn this talk we will consider two classical mathematical models of wine fermentation. The first model will describe the wine-making process that is used to produce dry wine. The second model will be obtained by introducing a term in the equation of the dynamics of the yeast. Thanks to this change it will be possible to inhibit the fermentation of the sugar and as a consequence a sweet wine will be obtained. We will first prove the existence, uniqueness, positiveness and boundedness of solutions for both models. Then we will pass to analyze the long-time dynamics. For the second model we will also provide estimates for the concentration of ethanol, nitrogen and sugar at the end of the process. Moreover, several numerical simulations will be provided to support the theoretical results.Ponencia Efecto de la rugosidad en el deslizamiento de un fluido sobre una pared(2001) Simon, Jacques; Casado Díaz, Juan; Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales; FQM131: Ec.diferenciales, Simulación Num. y Desarrollo SoftwareRecordamos resultados y presentamos problemas abiertos acerca de la influencia del perfil y la rugosidad de un cuerpo sólido sobre su resistencia al arrastre hidrodinámico. Mostramos además que, asintóticamente, un fluido no puede deslizarse sobre una pared recubierta de asperezas minúsculas si éstas son demasiado numerosas: en tal caso, se adhiere a la pared.Ponencia Convergencia de las ecuaciones de Navier-Stokes Globalmente Modificadas con retardo a las ecuaciones de Navier-Stokes(2011-09) Marín Rubio, Pedro; Márquez Durán, Antonio Miguel; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas DiferencialesEn esta comunicación demostramos que, bajo ciertas hipótesis, de una sucesión de soluciones del modelo Navier-Stokes Globalmente Modificado con retardo podemos extraer una subsucesión que converge en un sentido adecuado a una solución débil del correspondiente modelo de Navier-Stokes en dimensión tres. También se analiza el caso en el que aparecen retardos distintos en los problemas aproximantes.Ponencia Numerical methods for solving the Cahn-Hilliard equation and its applicability to mixtures of isotropic and nematic flows with anchoring effects(2016-05) Rodríguez Bellido, María Ángeles; Guillén González, Francisco Manuel; Tierra Chica, Giordano; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales, Simulación Num.y Desarrollo SoftwarePonencia Estudio de una ecuación del calor semilineal en dominios no-cilíndricos(2009-09) Marín Rubio, Pedro; Kloeden, Peter E.; Real Anguas, José; Ecuaciones diferenciales y Análisis numérico; FQM314: Análisis Estocástico de Sistemas DiferencialesEn esta comunicación presentaremos resultados de existencia y unicidad de soluciones que verifican una igualdad de energía para una ecuación semilineal en dominios no-cilíndricos (cf. [P. E. Kloeden, P. Marín-Rubio and J. Real, Pullback attractors for a semilinear heat equation in a non-cylindrical domain, J. Differential Equations 244 (2008), 2062–2090]) basándonos en algunas ideas de [M. L. Bernardi, G. A. Pozzi and G. Savaré, Variational equations of Schroedinger-type in noncylindrical domains, J. Differential Equations 171 (2001), 63–87. S. Bonaccorsi and G. Guatteri, A variational approach to evolution problems with variable domains, J. Differential Equations 175 (2001), 51–70]. En la prueba se usa un método de penalización para un problema más regular y paso al límite. Tras ello, y con hipótesis adicionales, se consiguen estimaciones uniformes que permiten estudiar el comportamiento asintótico del problema.Ponencia Equi-atracción y dependencia continua de atractores para ecuaciones con retardo(2007-09) Marín Rubio, Pedro; Kloeden, Peter E.; Ecuaciones diferenciales y Análisis numérico; FQM314: Análisis Estocástico de Sistemas DiferencialesEn esta comunicación se presentan brevemente los resultados del trabajo [P. E. Kloeden & P. Marín-Rubio. Equi-Attraction and the continuous dependence of attractors on time delays. Discrete Contin. Dyn. Syst. Ser. A.]: condiciones de equivalencia sobre la continuidad de atractores para semiflujos generados por ecuaciones diferenciales con retardo planteadas en (potencialmente) distintos espacios de fase. Dichas condiciones, basadas en el concepto de equi-atracción, son una extensión de trabajos previos debidos a Li y Kloeden (e.g. [D.S. Li & P.E. Kloeden, Equi-attraction and the continuous dependence of attractors on parameters, Glasgow Math. J., 46 (2004), 131–141]), y requieren previamente la inmersión de todos los sistemas dinámicos en un marco que los englobe, y la reinterpretación correcta de las condiciones entre los espacios originales y éste último. Se añaden ejemplos que ilustran la teoría.Ponencia Reduced basis method for the Smagorinsky model(2016) Chacón Rebollo, Tomás; Delgado Ávila, Enrique; Gómez Mármol, María Macarena; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas MedioambientalesWe present a reduced basis Smagorinsky model. This model includes a non-linear eddy diffusion term that we have to treat in order to solve efficiently our reduced basis model. We approximate this non-linear term using the Empirical Interpolation Method, in order to obtain a linearised decomposition of the reduced basis Smagorinsky model. The reduced basis Smagorinsky model is decoupled in a Online/Offline procedure. First, in the Offline stage, we construct hierarchical bases in each iteration of the Greedy algorithm, by selecting the snapshots which have the maximum a posteriori error estimation value. To assure the Brezzi inf-sup condition on our reduced basis space, we have to define a supremizer operator on the pressure solution, and enrich the reduced velocity space. Then, in the Online stage, we are able to compute a speedup solution of our problem, with a good accuracy.Ponencia Long-time behavior of a Cahn-Hilliard-Navier-Stokes vesicle-fluid interaction model(2015-06) Climent Ezquerra, María Blanca; Guillén González, Francisco Manuel; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulación Num.y Desarrollo SoftwarePonencia On the control of some systems modelling solidification processes and related phenomena(2009) Fernández Cara, Enrique; Camacho, G.; Boldrini, José Luiz; Caretta, B.; Cabrales, Roberto Carlos; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulación Num.y Desarrollo SoftwarePonencia Some inverse problems in elastography(2011) Fernández Cara, Enrique; Maestre Caballero, Faustino; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software; FQM309: Control y Homogeneización de Ecuaciones en Derivadas ParcialesPonencia Some recent results concerning the theoretical and numerical controllability of PDEs(2014) Fernández Cara, Enrique; Münch, Arnaud; Araujo de Souza, Diego; Dias Araruna, Fágner; Cardoso Santos, Mauricio; Limaco Ferrel, Juan; Dias Bezerra de Menezes, Silvano; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulación Num.y Desarrollo SoftwarePonencia On the Navier boundary condition for viscous fluids in a thin domain covered by very small asperities(2011) Suárez Grau, Francisco Javier; Ecuaciones Diferenciales y Análisis NuméricoPonencia Nuevos fenómenos en la controlabilidad exacta a cero de sistemas de EDP parabólicas(2014) González Burgos, Manuel; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software